Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main(void) {
  long long n, h;
  cin >> n >> h;
  double a = double(h / 2.0) / n;
  double lo = 0, sz = h;
  vector<double> cuts;
  double x;
  while (sz > 0) {
    x = lo + sz / 2.0;
    double base = x / h;
    double area = x * base * 0.5;
    if (area < a) lo += sz / 2.0;
    sz /= 2.0;
  }
  cuts.push_back(x);
  for (int i = 0; i < n - 2; i++) {
    lo = cuts.back(), sz = h - lo;
    while (sz > 0) {
      x = lo + sz / 2.0;
      double base = x / h;
      double area = x * base * 0.5 - (a * (i + 1));
      if (area < a) lo += sz / 2.0;
      sz /= 2.0;
    }
    cuts.push_back(x);
  }
  for (auto x : cuts) printf("%.15f ", x);
  puts("");
  return 0;
}